Convergence of a modified Samarskij's monotonic scheme on a smoothly condensing grid
type: Item
instance of: scholarly article
title: Convergence of a modified Samarskij's monotonic scheme on a smoothly condensing grid
zbMATH Open document ID: 0972.65045
published in: Computational Mathematics and Mathematical Physics
publication date: 2001-11-11T00:00:00Z
review text: A modified monotonic difference scheme on a nonuniform grid is used for approximating a singular perturbed second-order ordinary differential equation that degenerates into a first-order equation when the small parameter tends to zero. A certain optimal method for condensing the grid in the boundary layer and in the neighborhood of this layer is proposed. It is proved that this scheme converges uniformly with respect to the small parameter. The convergence rate is \(O(N^{-2})\), where \(N\) is the total number of grid points.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1472948
zbMATH Keywords: singular perturbation
zbMATH Keywords: small parameter
zbMATH Keywords: grid refinement
zbMATH Keywords: difference scheme
zbMATH Keywords: boundary layer
zbMATH Keywords: convergence
author: Vladimir B. Andreev
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1472948